It is well known that when a signal is input to a matched filter (matched to the input signal) then the output of the filter is the autocorrelation function of the signal. Also well known is that the autocorrelation function is the Fourier transform of the signal's power spectral density (PSD). A matched filter provides optimum (maximum) signal-to-noise ratio (SNR) at the peak of its autocorrelation function, and is consequently optimum for detecting the signal in noise.
A very common conventional radar waveform is the Linear FM (LFM) chirp signal. Such a signal can be readily generated by a variety of technologies, and is easily processed by a variety of techniques that ultimately implement a matched filter, or nearly so. However, since a LFM chirp waveform has nearly a rectangular PSD, its autocorrelation function exhibits a sinc( ) function shape, i.e. sin(x)/x, with its attendant problematic sidelobe structure.
Reducing the sidelobes of the matched filter output (actually, increasing the peak to sidelobe ratio) is typically accomplished by linear filtering the output, most often by applying window functions or data tapering during the processing. This additional filtering perturbs the matched filter result to reduce sidelobes as desired. However, since the cumulative filtering is no longer precisely matched to the signal, it necessarily reduces output SNR as well, typically by 1-2 dB (depending on the filtering or weighting function used).
It is well known that non-linear FM (NLFM) chirp modulation can advantageously shape the PSD such that the autocorrelation function exhibits substantially reduced sidelobes from its LFM counterpart. Consequently, no additional filtering is required and maximum SNR performance is preserved. The sidelobe reduction associated with NLFM chirp waveforms can yield a 1-2 dB advantage in SNR as compared to the output of an LFM waveform with equivalent sidelobe filtering. However, precision NLFM chirps are more difficult to design, produce, and process than LFM chirps.
Alternatives to NLFM modulation for shaping the PSD, such as amplitude tapering the transmitted signal, are problematic because efficient power amplification of the waveform typically necessitates operating the hardware in a nonlinear manner, e.g. operating the amplifiers in compression. This substantially reduces the ability to maintain precision amplitude tapering. Waveform phase remains unaffected by operating amplifiers in compression.
Radar design aspires to a NLFM waveform that is (1) easily produced, (2) easily processed, and (3) easily designed to meet target performance criteria, including bandwidth constraints and sidelobe reduction goals. The progress of technology now offers the possibility of addressing points (1) and (2). The advent of high-speed digital-to-analog converters (DACs) and high-speed large-scale field programmable gate arrays (FPGAs) currently facilitates generating high-performance precision digital LFM chirp waveforms. The high-speed FPGAs, together with conventionally available high-speed analog-to-digital converters (ADCs) facilitate direct sampling of fairly wide bandwidth signals. Modern high-speed processors permit the use of more complex filtering and detection algorithms.
However, the design of NLFM radar chirp waveforms, and the linkage between design and production of those waveforms, remain as challenges in the radar field. It is therefore desirable to provide solutions that address these and other challenges in the radar field.